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G-structures and Flavouring non-Abelian T-duality

Alejandro Barranco, Jerome Gaillard, Niall Macpherson, Carlos Nunez, Daniel C. Thompson

TL;DR

This work analyzes non-Abelian T-duality for ${\mathcal N}=1$ backgrounds, showing that dualising along SU(2) directions typically maps $SU(3)$-structure internal manifolds to $SU(2)$-structure ones and providing explicit pure-spinor transformation rules. It applies the framework to Klebanov--Witten, first in the unflavoured case and then with smeared D7 flavours, yielding new flavoured type IIA solutions with D8 and D6 charges. The authors derive the dual RR potentials, RR fluxes, and calibrations within the pure-spinor formalism, clarifying charge redistribution under $B$-field transformations and the role of generalized calibrations for SUSY brane embeddings. Overall, the paper offers a geometric, SUSY-aware route to generate and analyse flavoured holographic backgrounds with potential dual field theories and RG-flow phenomena.

Abstract

We examine non-Abelian T-duality on backgrounds preserving N=1 supersymmetry. We show how backgrounds with SU(3)-structure are mapped to backgrounds with SU(2)-structure. We provide the transformation rules for the corresponding pure spinors. We use these techniques to construct new flavoured solutions of type IIA supergravity.

G-structures and Flavouring non-Abelian T-duality

TL;DR

This work analyzes non-Abelian T-duality for backgrounds, showing that dualising along SU(2) directions typically maps -structure internal manifolds to -structure ones and providing explicit pure-spinor transformation rules. It applies the framework to Klebanov--Witten, first in the unflavoured case and then with smeared D7 flavours, yielding new flavoured type IIA solutions with D8 and D6 charges. The authors derive the dual RR potentials, RR fluxes, and calibrations within the pure-spinor formalism, clarifying charge redistribution under -field transformations and the role of generalized calibrations for SUSY brane embeddings. Overall, the paper offers a geometric, SUSY-aware route to generate and analyse flavoured holographic backgrounds with potential dual field theories and RG-flow phenomena.

Abstract

We examine non-Abelian T-duality on backgrounds preserving N=1 supersymmetry. We show how backgrounds with SU(3)-structure are mapped to backgrounds with SU(2)-structure. We provide the transformation rules for the corresponding pure spinors. We use these techniques to construct new flavoured solutions of type IIA supergravity.

Paper Structure

This paper contains 14 sections, 144 equations.

Table of Contents

  1. Introduction
  2. Non-Abelian T-duality
  3. G-structures and their transformations
  4. Example 1: Unflavoured Klebanov--Witten and its T-Dual
  5. Example 2: Flavoured Klebanov Witten and its T-Dual.
  6. The T-dual
  7. A nice subtlety.
  8. Potentials, $SU(2)$-structure and Calibration.
  9. Analysis of the dualised geometry
  10. Discussion and Conclusions
  11. Appendix: Supergravity without Sources: conventions
  12. Appendix: On $SU(2)$-Structures in six dimensions
  13. Appendix: Some Details of the Flavoured $SU(3)$ and $SU(2)$-structure solutions
  14. Analysis of the generated background.